Q. 0.14189189189… can be expressed as a rational number
A) $\frac{7}{3700}$
B) $\frac{7}{50}$
C) $\frac{525}{111}$
D) $\frac{21}{148}$
Explanation
(d)
$0.14189189189\ldots$
$= 0.14 + 0.00189 + 0.00000189 + \ldots$
$= \frac{14}{100} + 189\left\lbrack \frac{1}{10^{5}} + \frac{1}{10^{8}} + ...\infty \right\rbrack$
$= \frac{7}{50} + \frac{189}{999 \times 100}$
$= \frac{7}{50} + \frac{7}{3700} = \frac{21}{148}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.